Okay. I get why they chose Jack. Because no one knows who it is. I agree there is way worse killers but think of one that EVERYONE knows. It's Jack the Ripper.
As for the fight, it makes sense to me because Hercules would be hesitant to defeat anyone who is an outstanding person. They want a "good show", right? If Hercules is truly "justice" he won't truly kill. Many mistakes justice for anger.
As for me, I choose mercy over justice